The temperature of a gas placed in an open container is raised from 27 °C to 227 °C. The percent of the original amount of the gas expelled from the container will be

Options

A. 20
B. 40
C. 60
D. 80

Explanation

To solve the problem of determining the percentage of the original amount of gas expelled from an open container when the temperature is raised from 27 °C to 227 °C, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Celsius to Kelvin**:
- The initial temperature \( T_1 \) is 27 °C. To convert this to Kelvin:
\[ T_1 = 27 + 273 = 300 \, \text{K} \]
- The final temperature \( T_2 \) is 227 °C. To convert this to Kelvin:
\[ T_2 = 227 + 273 = 500 \, \text{K} \]

2. **Use the Ideal Gas Law for Open Container**:
- For an open container, the relationship between the initial and final amounts of gas can be expressed as:
\[ n_1 T_1 = n_2 T_2 \]
- Here, \( n_1 \) is the initial amount of gas, \( n_2 \) is the amount of gas left after heating, \( T_1 \) is the initial temperature, and \( T_2 \) is the final temperature.

3. **Set Initial Amount of Gas**:
- Let the initial amount of gas \( n_1 = x \).

4. **Substitute Values into the Equation**:
- Substitute \( n_1 \), \( T_1 \), and \( T_2 \) into the equation:
\[ x \cdot 300 = n_2 \cdot 500 \]

5. **Solve for \( n_2 \)**:
- Rearranging the equation gives:
\[ n_2 = \frac{x \cdot 300}{500} \]
- Simplifying this:
\[ n_2 = \frac{3x}{5} \]

6. **Calculate the Amount of Gas Expelled**:
- The amount of gas expelled \( n_{\text{expelled}} \) is the initial amount minus the amount left:
\[ n_{\text{expelled}} = n_1 - n_2 = x - \frac{3x}{5} \]
- This simplifies to:
\[ n_{\text{expelled}} = \frac{5x}{5} - \frac{3x}{5} = \frac{2x}{5} \]

7. **Calculate the Percentage of Gas Expelled**:
- The percentage of the original amount expelled is given by:
\[ \text{Percentage expelled} = \left( \frac{n_{\text{expelled}}}{n_1} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Percentage expelled} = \left( \frac{\frac{2x}{5}}{x} \right) \times 100 \]
- This simplifies to:
\[ \text{Percentage expelled} = \frac{2}{5} \times 100 = 40\% \]

### Final Answer:
The percent of the original amount of the gas expelled from the container is **40%**.